Put turnips in a large pot; add water to cover. Bring to a boil, cover and boil 10 minutes or until tender. Drain in a colander (don't wash pot).

In a food processor, process half the turnips, butter and milk at a time until smooth. Scrape both batches into the cooking pot; stir in salt and pepper. Spread in prepared baking dish.

Onions: Toss onion rings with flour to coat.

Pour oil to a depth of 3 inches into a 3 to 3½-quart saucepan. (If using an electric deep fryer, follow manufacturer's instructions.) Heat until oil registers 375°F on a deep-fat frying thermometer or until a cube of white bread dropped in the oil becomes golden in 1 minute.

Shake excess flour off onions. Using a large metal slotted spoon, carefully place onions in oil, no more than 2 spoonfuls at a time. Fry 1 minute or until golden brown. Remove with slotted spoon to paper towels to drain. Sprinkle with salt and pepper. Repeat with remaining onions, keeping oil temperature near 375°F.

To serve: Heat oven to 350°F. Bake purée 20 minutes until heated through, scattering onions on top after 15 minutes. Sprinkle with parsley.If you don't have a food processor, you can mash the vegetables with a potato masher, but the mixture may not be as smooth.

Make Ahead: The vegetable purée can be made through Step 3 up to 2 days ahead. Cover tightly and refrigerate. Bring to room temperature before heating. The onions can be prepared through Step 6 up to 1 day ahead. Cover when completely cool and refrigerate. Bring to room temperature before reheating.

Carrot Variation: Use 4 pounds carrots instead of turnips. Add ½ teaspoon ground ginger along with the salt and pepper. Proceed as directed.

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